{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

slides1026

# slides1026 - CS 290H 26 October Sparse approximate inverses...

This preview shows pages 1–5. Sign up to view the full content.

CS 290H 26 October CS 290H 26 October Sparse approximate inverses, support graphs Sparse approximate inverses, support graphs Homework 2 due Mon 7 Nov. Sparse approximate inverse preconditioners Introduction to support theory

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Preconditioned conjugate gradient iteration Preconditioned conjugate gradient iteration x 0 = 0, r 0 = b, d 0 = B -1 r 0, y 0 = B -1 r 0 for k = 1, 2, 3, . . . α k = (y T k-1 r k-1 ) / (d T k-1 Ad k-1 ) step length x k = x k-1 + α k d k-1 approx solution r k = r k-1 α k Ad k-1 residual y k = B -1 r k preconditioning solve β k = (y T k r k ) / (y T k-1 r k-1 ) improvement d k = y k + β k d k-1 search direction Several vector inner products per iteration (easy to parallelize) One matrix-vector multiplication per iteration (medium to parallelize) One solve with preconditioner per iteration (hard to parallelize)
Sparse approximate inverses Sparse approximate inverses Compute B -1 A explicitly Minimize || A B -1 – I || F (in parallel, by columns) Variants: factored form of B -1 , more fill, . . Good: very parallel, seldom breaks down Bad: effectiveness varies widely A B -1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Support Graph Preconditioning Support Graph Preconditioning +: New analytic tools, some new preconditioners +: Can use existing direct-methods software -: Current theory and techniques limited CFIM: Complete factorization of incomplete matrix
This is the end of the preview. Sign up to access the rest of the document.
• Fall '09
• Chong
• Preconditioner, Conjugate gradient method, Positive-definite matrix, maximum-weight spanning tree, Tree Preconditioner, Sparse approximate inverses

{[ snackBarMessage ]}

### Page1 / 16

slides1026 - CS 290H 26 October Sparse approximate inverses...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online